DEVELOPMENT OF A FLUORESCENT CRYOCOOLER

• Abstract
• Introduction
• Anti-Stokes Fluorescent Cooling
• First-Generation Fluorescent Cryocooler
• Future Directions
• Conclusions
• References

Recent work at Los Alamos National Laboratory has demonstrated the physical principles of a new type of solid-state cryocooler based on anti-Stokes fluorescence. Design studies indicate that a vibration-free, low-mass "fluorescent cryocooler" could operate for years with efficiencies and cooling powers comparable to current commercial systems. This paper presents concepts for a fluorescent cryocooler, design considerations, and expected performance.

Recent laboratory measurements have demonstrated laser-induced anti-Stokes fluorescent cooling of a solid [1]. Combining this laboratory work with computer simulations and information on available technology, we expect that a practical, first-generation, all-solid-state fluorescent cryocooler will have the following properties:

• no vibrations
• does not produce and is not susceptible to electromagnetic interference
• cools to 77 K
• is ~1% efficient (DC power to cooling power)
• weighs less than 3 kg/W
• has a lifetime of 10 years continuous operation.

This first-generation cryocooler will employ material with a demonstrated fluorescent cooling capability (ytterbium-doped ZBLANP). With improved cooling materials and designs, future cryocoolers could be over twice as efficient at 77 K and cool to lower temperatures.

Anti-Stokes fluorescence is the phenomena in which a substance that is excited by radiation at one wavelength fluoresces at a shorter wavelength. This results in more energy being radiated than is absorbed for each photon. Utilizing this process for cooling may, at first, appear to violate common sense: a multi-watt laser is focused into a mostly transparent material, and yet the material cools. A closer look at a specific cooling process reveals how it works. Consider a glass doped with a rare-earth ion that has spectrally broad ground and excited states (see Fig. 1). Each energy state, or manifold, consists of several closely spaced levels that are in thermal equilibrium among each other. (Since we will be discussing glasses the energy levels are actually inhomogeneously broadened bands, but for simplicity we will refer to them as discrete levels.) When ions are radiatively pumped from the top of the ground- state manifold to the bottom of the excited-state manifold (process 1), the thermal equilibrium within each manifold is upset. The upper level of the ground-state manifold is underpopulated and the lower level of the excited-state manifold is overpopulated. Both manifolds quickly return to equilibrium by absorbing phonons (heat) from the surroundings (process 2). At some later time, the ions de-excite by emitting photons (process 3). The fluorescent photons remove both the pump photon energy and the absorbed phonon energy from the system. The net result of this process is the removal of heat from the material.

In the ideal case, where there are no nonradiative relaxations from the excited- to the ground-state manifolds, there will be one fluorescent photon for each pump photon and each fluorescent photon carries off, on average, thermal energy equal to the difference between the pump-photon energy and the mean fluorescent-photon energy. The fluorescent cooling power, P, is thus proportional to the absorbed pump power, P, and to the average difference in the photon energies of the pump and fluorescence radiation. In terms of wavelength, the cooling power can be written as:

,

where is the wavelength of the incident pump radiation and is the wavelength corresponding to the mean fluorescent-photon energy.

Overall Design:

An especially interesting application of a solid-state fluorescent cryocooler is for use in space, where performance attributes are critical. In these applications, fluorescent cryocoolers would be a valuable asset because they are vibration-free, low-mass, rugged, long-lived, and efficient.

Figure 2: A design for a fluorescent cryocooler.

Figure 2 illustrates one design for a fluorescent cryocooler that might be used in space. It is based on using an ytterbium-doped heavy-metal-fluoride glass as the fluorescent cooling element. Preliminary studies have demonstrated that one such material, ZBLANP:Yb, is an efficient fluorescent cooler [1].

Our initial design utilizes a combination of diode lasers coupled with an ytterbium-fiber laser to efficiently produce pump radiation at the desired wavelength (see Fig. 2). The fiber carrying the pump radiation passes through the wall of the cryocooler and into a cylindrical block of ZBLANP:Yb, the cooling element at the heart of the device (see Fig. 3).

Figure 3: Schematic of the cooling element and cold finger design. The input laser light is shown as the solid lines and the fluorescence as the dashed ones. Violet-colored areas indicate the regions where the fluorescent radiation is most intense. White areas are in the shadow of the dielectric mirrors. These shadowed regions are not completely free of fluorescent radiation, however, due to the bandpass of the dielectric mirrors. Hence, a metal mirror and baffles are required to fully eliminate fluorescent-radiation heat loading of the object to be cooled.

Dielectric mirrors that reflect the pump radiation are deposited on both ends of the cooling element. The pump radiation enters the cooling element through a small hole in one of the mirrors. It is largely beamed along the axis of the cylinder and is repeatedly reflected from the dielectric mirrors and from the sides of the glass cylinder (by total internal reflection). Ultimately, the pump radiation is absorbed by Yb ions, and the doped glass cools as it fluoresces. Most of the isotropic fluorescent radiation escapes from the cooling element and is absorbed by the warm walls of the cooling chamber. On the back of one of the dielectric mirrors a transparent connection and metal mirror are attached to create a completely shadowed region where the cold finger is located.

Each of the components of the fluorescent cryocooler must be precisely engineered in order to produce an effective device. We now examine some the considerations involved in designing the key components and how these choices can affect the overall performance of the cooler.

Cooling Element Composition:

The two essential requirements for a fluorescent cooling element are that it exhibit anti-Stokes fluorescence and that the resulting radiation-induced cooling is not severely degraded by heating from nonradiative decays. Both of these requirements are well satisfied by ZBLANP:Yb. The Yb ion has a simple energy level structure consisting of a ground-state and a single excited-state manifold at ~1000 nm. The room temperature fluorescence and absorption spectra of ZBLANP:Yb shown in Fig. 4 indicate that anti-Stokes fluorescence is achievable with this material. Since the mean energy of the fluorescent photons is at = 995 nm, the glass cools whenever the excitation is pumped with radiation having a wavelength > 995 nm, in accordance with Eq. (1). The absorption spectrum shows that it is indeed possible to pump ZBLANP:Yb at such long wavelengths.

Figure 4: Fluorescence and absorption spectra of Yb in ZBLANP.

It only takes a few phonon-emitting, nonradiative decays from the excited-state to the ground-state manifolds to overwhelm the fluorescent cooling. In pure ZBLANP:Yb this is not a problem. The radiative lifetime of the upper manifold is ~2 ms, whereas the nonradiative decay lifetime, which involves the simultaneous emission of more than 15 phonons, is estimated to be greater than a year. If multiphonon emission were the only nonradiative process, essentially all of the decays would occur radiatively.

Nonradiative transitions can be a problem, however, when contaminants are present. An excited Yb ion can de-excite by transferring its energy to a nearby contaminant ion such as Er, Dy, Sm, Fe, etc. These impurity ions can quickly decay nonradiatively, producing heat. The severity of this problem is amplified by excitation migration in which excitations move between neighboring Yb ions until it finds and is quenched by another impurity ion. Extremely pure materials are thus needed to produce an effective cooling element.

The absorption and fluorescence spectra vary with temperature since they depend on the populations of each level in the manifolds. At low temperatures, the populations of the higher-lying energy levels in the ground- state manifold decrease, thereby reducing the absorptivity at long wavelengths. Similarly, the decrease in the population of the upper levels in the excited-state manifold at low temperatures reduces the fluorescence at short wavelengths. As one might therefore expect, the net effect of a reduced temperature is that it is more difficult to achieve anti-Stokes fluorescent cooling.

Figure 5: Calculated cooling efficiency versus temperature for a 5 m and a 25 m pathlength of 2% Yb in ZBLANP.

We have simulated the temperature response of ZBLANP:Yb using energy levels from measured absorption and fluorescence spectra. Assuming a Boltzmann distribution for the population of each level in the two manifolds, we model the widths and transition probabilities for transitions between each of the states. Our calculations reproduce the observed room-temperature fluorescence and absorption spectra and simulate the behavior at other temperatures. We find that the mean fluorescent-photon energy shifts to longer wavelengths and the absorption spectrum shifts to shorter wavelengths as the temperature decreases. While these two effects reduce the anti-Stokes fluorescence, useful cooling efficiency can still be achieved using ZBLANP:Yb at temperatures of as low as 50 K (see Fig. 5).

Radiation Trapping:

The primary considerations in designing the cooling element, besides the choice of material, are geometrical. The cooling element must completely absorb the pump radiation while allowing the fluorescent radiation to escape.

To most efficiently utilize the pump laser power, the radiation should have the longest possible wavelength, in accordance with Eq. (1), and it should be completely absorbed in the cooling material. Since the absorptivity decreases at long wavelengths, simultaneously satisfying these two conditions requires that the radiation be trapped in the cooling element until it is absorbed. In the first-generation fluorescent cryocooler design, we propose to use dielectric mirrors on the ends of the cooling element to trap the pump radiation. As Fig. 3 shows, the laser radiation enters the cooling element in a narrow cone aligned with the axis of the cylindrical element. The divergence is small enough that the light is almost perfectly reflected from the dielectric mirrors at the ends or by total internal reflection from the sides of the cooling element. Initial tests indicate that this scheme is workable. The trapping efficiency is determined by the quality of the glass, the mirror construction, and the ratio of the mirror area to the area of the entrance hole through which the pump light enters. Several practical considerations determine the currently attainable trapping efficiency:

• Dielectric mirrors can be made that reflect 99.97% of the incident radiation for angles within 30 degrees of normal. This is adequate for exit angles of standard fibers (N.A. = 0.22, implying exit half-angles < 13 degrees).

• Because of the entrance hole, the light leakage per reflection is equal to the ratio of the area of the hole to that of the mirror. The current design uses a 0.1 mm diameter hole and a 30 mm diameter mirror to give us a leakage per reflection ratio of 0.000 011.

• Imperfections in the cooling element or the mirrors may scatter some radiation out of the "trapping cone" before it is absorbed.

We estimate that with current technology the pump radiation can be trapped for at least several hundred passes (~5 m pathlength in our design) and possibly for 1000 passes (~25 m pathlength) through the sample. As can be seen in Fig. 5, this is a critical design consideration and further studies on trapping mechanisms are needed.

The fluorescent radiation is emitted isotropically in the cooling element, and most of it is able to escape without any reflections. About 25% of the fluorescence will be trapped by internal reflections and by the dielectric mirrors and will be reabsorbed in the Yb. During subsequent fluorescence most of this radiation will escape. This repeated absorption will not seriously degrade the performance of the system because the absorbed and re-emitted light have similar mean energies.

Mass of Cooling Element and Cooler:

Figure 6: The minimum mass of the cooling element for a half-watt ZBLANP:Yb fluorescent cryocooler.

The maximum heat which a fluorescent cooler can extract depends on the mass of the cooling element, the Yb concentration, and the operating temperature. As an example, Fig. 6 gives the required mass of the cooling element for a 0.5 W unit with 2 wt % concentration of Yb. For the fluorescent cryocooler to operate at 77 K, the cooler element would have to be at least 80 g; this would corresponding to a cylinder with a height and diameter of 3 cm.

The remaining mass of the cryocooler is composed of the outer wall, diode lasers, heat sinks, and control electronics. The outer wall must be able to transport the waste fluorescent heat away. Similarly, heat sinks must be implemented to remove the heat generated by the diode lasers. These thermal conduction paths could be constructed from diamond-coated aluminum or copper. The mass of the outer wall would then be roughly 350 g. Each laser diode set (8 are needed to ensure a 10 year lifetime) and heat sink would have a mass of about 100 g. The laser-diode control electronics could be made very simple in a spacecraft system, since DC power is readily available, and thus should weigh in at only 300 g. The total mass estimate for a 0.5 W fluorescent cryocooler is thus about 1.5 kg for a first-generation system. By integrating the cryocooler into the overall spacecraft design, a cryocooler system might be constructed with a mass as small as several hundred grams.

Pump Radiation Source:

A cryocooler for use in space applications requires a radiation source that is compact, efficient, reliable, and rugged and has the necessary power and wavelength. Fortunately, recent developments in diode lasers and solid-state lasers have made a number of options available. The radiation source we are currently considering is a diode pumped ytterbium-fiber laser.

To produce 0.5 W of cooling power at 77 K, the cooler needs ~20 W of laser light at 1020 nm. Commercially available high efficiency diode lasers can produce tens of watts of c.w. power at 980 nm with ~60% efficiency (DC power to light). Ytterbium-fiber lasers have been made that can convert the 980 nm radiation to 1020 nm radiation with ~80% efficiency [2]. Allowing for an ~80% efficiency in the optical couplings, we need ~50 W of electrical power to run the 0.5 W cooler. This means that, for the first-generation fluorescent cryocooler, the DC power to cooling power efficiency would be ~1%.

The lifetime of the fluorescent cryocooler will be limited by the lifetimes of the diode lasers. Currently, commercial diode lasers have mean times to failure of ~14 months. The lifetime of the cryocooler can be extended by combining multiple, redundant, relatively low-power diode lasers. This would have the added advantage of distributing the heat load. For a system to achieve a ten year lifetime, eight sets of diodes would be required.

Shielding and Shadowing:

An important part of the design of an effective fluorescent cryocooler is controlling the flow of fluorescent radiation and the thermal radiation from the warm walls of the cooler.

To decrease the heat load on the cooling element from the thermal radiation of the walls, layers of shielding are inserted between these components (see Figs. 2 and 3). The shielding material must be transparent to the fluorescence, allowing this radiation to escape and be absorbed on the walls. On the other hand, the shields should reflect or absorb the thermal radiation from the walls, to prevent it from reaching the cooling element. One possibile shielding material is silica glass coated on the wall sides with a thin layer of titanium dioxide. Since titanium dioxide is highly reflective from 8 to 13 µm [4], these shields would be thermally reflective on the surfaces facing the walls and roughly blackbody emitters on their inner surfaces. Each shield of this type would reduce the radiative loading by unity minus its reflectivity. For example, a 60% reflecting surface on three shields would reduce the heat load by a factor of ~15.

The cold finger and cooled instruments have to be well protected from both the fluorescent and thermal radiation fields. Placing a curved metal mirror behind and in thermal contact with one of the dielectric mirrors would create an area completely shadowed from the fluorescence (see Fig. 3). The object to be cooled could be attached to this dark area.

Future generations of fluorescent cryocoolers should benefit from improved cooling element materials and from new developments in diode lasers.

Cooling Element Composition:

The proposed design of our first-generation fluorescent cryocooler employs an Yb doped glass which has an exceedingly simple energy-level structure. However, numerous other dopant-host combinations are possible. Figure 7 illustrates the energy levels of some rare-earth ions which are potential fluorescent coolants.

Figure 7: Energy-level diagram for several rare earth ions [3]. The arrows show the transitions that could be used for cooling.

The cooling transitions must have the property that the radiative lifetimes (which can be on the order of milliseconds for rare-earth ions) must be much larger than the multiphonon nonradiative relaxation times (which depend on the host material: see Fig. 8). Dopant-host combinations such as ZBLANP:Tm and LaBr:Dy appear promising due to their large multiphonon energy gaps (see Figs. 7 and 8). Owing to the longer laser wavelengths required to pump these ions, these combinations should have higher overall cooling efficiency than does ZBLANP:Yb. For example, since the spectral widths of the Tm manifolds are roughly the same as those of Yb (namely ~500 cm), the overall efficiency should increase by the ratio of the energy gaps between the ground- and excited-state manifolds.

Figure 8: Phonon emission rate versus energy gap for several glasses (solid lines) and crystals (dashed lines) at room temperature [6].

Recent developments in laser diode technology may make higher efficiency sources at more wavelengths readily available [5]. In particular, InGaAsP high-power laser diodes potentially have lifetimes of 10 years or more. Additionally, these diodes may have enough wavelength flexibility to pump an Yb fluorescent cryocooler directly, thus obviating the need for an intermediary ytterbium-fiber laser.

Laboratory data has proven the feasibility of cooling macroscopic solid objects via anti-Stokes fluorescence. We have studied the possibility of using this phenomenon to produce a practical cryocooler. With current technology, a fluorescent cryocooler that generates 0.5 W of cooling power at 77 K appears feasible. This first-generation cryocooler should be ~1% efficient, induce no vibrations, have a long life, and have a mass of ~1.5 kg. Future systems could be at least twice as efficient and be operational at significantly lower temperatures. A small cryocooler of this sort would be well suited for operation in space.

[1] Epstein, R.I., Buchwald, M.I., Edwards, B.C., Gosnell, T.R., and Mungan, C.E., Observation of laser-induced fluorescent cooling of a solid, Nature 377, 500 (1995).

[2] Hanna, D. and Tropper, A., Laser Focus World (May 1995) p.123.

[3] Macfarlane, R.M. and Shelby, R.M., in Spectroscopy of Solids Containing Rare Earth Ions, eds. A.A. Kaplyanskii and R.M. Macfarlane (North Holland, Amsterdam, 1987) p. 51.

[4] Browder, J.S., Ballard, S.S., and Klocek, P., in Handbook of Infrared Optical Materials, ed. P. Klocek (Marcel Dekker, NY, 1991) p. 141.

[5] Razeghi, M., Optics & Photonics News (August 1995) p. 16.

[6] Weber, M. J., ed., CRC Handbook of Laser Science and Technology - Supplement 1: Lasers, (CRC Press, Boca Raton, 1991).

Acknowledgments:

We thank T. Pfafman, and W.R. Scarlett for helpful discussions and comments. This work has been carried out under the auspices of the U.S. Department of Energy.